The First Vatican Council has defined as
"a divinely revealed dogma" that "the Roman Pontiff, when he speaks
ex cathedra -- that is, when in the exercise of his office as pastor
and teacher of all Christians he defines, by virtue of his supreme
Apostolic authority, a doctrine of faith or morals to be held by the
whole Church -- is, by reason of the Divine assistance promised to
him in blessed Peter, possessed of that infallibility with which the
Divine Redeemer wished His Church to be endowed in defining doctrines
of faith and morals; and consequently that such definitions of the
Roman Pontiff are irreformable of their own nature (ex sese) and not
by reason of the Church's consent"
--Infallibility
at the Catholic Encyclopedia [1913]

Infallibility belongs in a special way to the pope as head of
the bishops (Matt. 16:17-19; John 21:15-17). As Vatican II remarked,
it is a charism the pope "enjoys in virtue of his office, when,
as the supreme shepherd and teacher of all the faithful, who confirms
his brethren in their faith (Luke 22:32), he proclaims by a definitive
act some doctrine of faith or morals. Therefore his definitions,
of themselves, and not from the consent of the Church, are justly
held irreformable, for they are pronounced with the assistance of
the Holy Spirit, an assistance promised to him in blessed Peter."
--Papal
Infallibility - at Catholic Answers

Papal infallibility is one of the great differences between Catholicism
and Protestantism. Very few seem to be aware of the awesome implications
of this Catholic dogma. Hopefully, this brief summary will illuminate
them. Regarding papal infallibility the present-day Roman Catholic
Church says... --Papal
Infallibility - by Dan Corner

Papal Infallibility at the First Vatican Council in 1870

To the mind of the general reader, mention
of the Vatican Council will usually recall two facts: that it was
the occasion of the definition of the doctrine popularly called Papal
Infallibility, and that many of the bishops present were opposed to
the definition. The more erudite will add that their opposition was
not to the doctrine itself, but to the policy of choosing this present
moment to proclaim it--the definition, they would say, was held not
"opportune." ... The leading critics of the "definition policy" were
French, German, and Hungarian
--CHAPTER
20

Following the first Vatican Council, 1870, a dissent, mostly among
German, Austrian and Swiss Catholics, arose over the definition
of Papal Infallibility. The dissenters, holding the General Councils
of the Church infallible, were unwilling to accept the dogma of
Papal Infallibility. Many of these Catholics formed independent
communities which became known as the Old
Catholic Church.

At the First Vatican Council he was one of the most notable opponents
of papal infallibility, and distinguished himself as a speaker.
The pope praised Strossmayer's "remarkably good Latin." A speech
in which he defended Protestantism made a great sensation. Afterwards
another speech, delivered apparently on 2 June, 1870, was imputed
to him. It is full of heresies and denies not only infallibility
but also the primacy of the pope. The forger is said to have been
a former Augustinian, a Mexican named Dr. José Agustín de Escudero.
--Joseph
Georg Strossmayer, the Catholic Encyclopedia, 1913

Power and the Papacy : The People and Politics Behind the Doctrine
of Infallibility
by Robert McClory (a reporter for US Catholic and a professor of Journalism
at Northwestern University) ISBN 0-7648-0141-4 (October 1997) Published
by Triumph, An Imprint of Liguori Publications [amazon.com]